motivated by e-mail
Here's what we want to do:
- Download ten years worth of daily prices for some stock, say GE.
- Generate a distribution of daily returns, like Figure 1.
- Apply this distribution of returns to a fictitious stock whose current price is, say $10.
This fictitious stock has nothing to do with GE stock.
Its evolution in time just uses the GE return distribution.
- Pick a number of days into the future, say 30.
- Select 30 returns at random, from the return distribution
(as in Fig. 1).
- See what happens to your $10 stock, after 30 days.
- Repeat steps 5 and 6 a jillion times and generate a probability distribution of prices, 30 days in the future.
| Figure 1 |
>And that's exact?
Are you kidding? To be exact you'd need this.
It's an estimate of a future stock price assuming the historical return distribution of GE stock is relevant.
Now that you have an estimate ...
>Is there a spreadsheet?
Yes. Patience!
Having an estimate of a future price such as Figure 2, you might use it to estimate the value of a stock option, for example.
In Fig. 2, the red dot is the current price that you've entered.
>Options?
Black-Scholes says:
Call Premium = S*NORMSDIST((LN(S/K)+(R+V^2/2)*T)/(V*SQRT(T)))
- K*EXP(-R*T)*NORMSDIST((LN(S/K)+(R+V^2/2)*T)/(V*SQRT(T))-V*SQRT(T))
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| Figure 2 |
>Huh?
The various parameters involved are explained here and ...
>And the spreadsheet?
>That's so confusing that ...
There's an Explain sheet which looks like this.
>What about that option stuff?
Yeah, it's there, too ... and looks like this:
You stick in the Strike Price etc. and it calculates the option premium (a la Black-Scholes).
You also get the probability of achieving some Wished-for Stock Price.
In Fig. 3, that's the Break-even stock price, namely Strike + Premium
... and the probability of achieving this in 30 days is 34.7%.
>And that's exact?
Of course! Would I lie to you?
| Figure 3 |
for Part II
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